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Monte Carlo Simulation of Order-Disorder Phenomena in Binary Alloys

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Structural and Phase Stability of Alloys

Abstract

An introduction is given into the Monte Carlo technique of phase diagram calculations. Beside the standard approaches used to determine first and second order phase transitions, a most promising development is discussed, namely the analysis of the probability distributions by histograms. Applications to real alloys are considered, such as the decomposition in Cu-Co and Cu-Ni, the short-range order and critical scattering in Cu-Au type alloys, the phenomenon of surface induced order in Cu-Au models having a free (100) surface, and the interplay of magnetism and chemical ordering in Fe-Ál.

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References

  1. K. Binder,J. Comput. Phys. 59, 1 (1985).

    Article  Google Scholar 

  2. K. Binder in Festkörperprobleme (Advances in Solid State Physics), edited by P. Grosse, Vieweg, Braunschweig, 1986. Vol. 26, p.133.

    Google Scholar 

  3. K. Binder in International Meeting on Advances on Phase Transitions and Disorder Phenomena in Amalfi June 1986, edited by G. Busiello, L. De Cesare, F. Manchini, and M. Marinaro, World Scientific, Singapore, 1987. p. 1.

    Google Scholar 

  4. The Monte Carlo Method in Statistical Physics,2nd ed, edited by K. Binder, Springer-Verlag, Berlin, 1986).

    Google Scholar 

  5. Applications of the Monte Carlo Method Method in Statistical Physics,2nd ed, edited by K. Binder, Springer-Verlag,Berlin,1987.

    Google Scholar 

  6. The Monte Carlo Method in Condensed Matter Physics,edited by K. Binder, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  7. V. Gerold and J. Kern, Acta Metall. 35, 393 (1987).

    Article  Google Scholar 

  8. W. Schweika and H. G. Haubold, Phys. Rev. B37, (1988) 9240

    Google Scholar 

  9. W. Schweika, in Alloy Phase Stability,edited by G. M. Stocks and A. Gonis, Kluwer Acad. Publ., Dordrecht, 1989. Proc. NATO ASI, Maleme, 1987.

    Google Scholar 

  10. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 21 108 (1953).

    Article  Google Scholar 

  11. R. J. Glauber, J. Math. Phys. 4, 294 (1963).

    Article  Google Scholar 

  12. K. Kawasaki in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green, Academic Press, New York, 1972. Vol. 2, p.443.

    Google Scholar 

  13. M. Creutz, Phys. Rev. D36, 515 (1987).

    Google Scholar 

  14. S. L. Adler, Phys. Rev. D38, 1349 (1988).

    Google Scholar 

  15. R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987).

    Article  Google Scholar 

  16. S. Wansleben, Comp. Phys. Comm 43, 315 (1987).

    Article  Google Scholar 

  17. N. Ito and Y. Kanada, Supercomputer 25, 3, 31 (1988).

    Google Scholar 

  18. H. O. Heuer, Europhys. Lett. 12, 551 (1990); to appear in Comput. Phys. Comm.

    Article  Google Scholar 

  19. S. Kirkpatrick and E. Stoll, J. Comp. Phys. 40, 517 (1981).

    Article  Google Scholar 

  20. F. James, Repts. Prog. Phys. 43, 1145 (1980).

    Article  Google Scholar 

  21. F. Livet and M. Bessiere, J. Phys. (Paris) 48, 1703 (1987).

    Article  Google Scholar 

  22. A. M. Ferrenberg, D. P. Landau, and K. Binder J. Stat. Phys. 63 867 (1991).

    Article  Google Scholar 

  23. G. Tammann and W. Oelsen, Z. Anorg. Chem. 186 260 (1930).

    Google Scholar 

  24. M. E. Fisher, Proceedings of the International Summer School Enrico Fermi,Course 51, Academic Press, New York, 1971.

    Google Scholar 

  25. M. E. Fisher, in Critical Phenomena, edited by M. S. Green, Academic Press, New York, 1971.

    Google Scholar 

  26. M. N. Barber, in Phase Transitions and Critical Phenomena, eds. C. Domb and J. L. Lebowitz, Academic Press, New York, 1983, Vol. 8, p. 145.

    Google Scholar 

  27. V. Privman and M. E. Fisher, J. Stat. Phys. 33 385 (1983); Phys. Rev. B32 447 (1985).

    Google Scholar 

  28. K. Binder, Z. Phys. B43 119 (1981).

    Article  Google Scholar 

  29. K. Binder, D. P. Landau, Phys. Rev. B30 1477 (1984).

    Google Scholar 

  30. K. Binder, Rep. Prog. Phys. 50, 783 (1987).

    Article  Google Scholar 

  31. A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, (1988).

    Google Scholar 

  32. R. H. Swendsen, J.-S. Wang and A. M. Ferrenberg, The Monte Carlo Method in Condensed Matter Physics,edited by K. Binder, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  33. A. M. Ferrenberg and D. P. Landau, Phys. Rev. B 44, 5081 (1991).

    Article  Google Scholar 

  34. A. M. Ferrenberg, D. P. Landau, and P. Peczak, J. Appl. Phys. 69 6153 (1991).

    Article  Google Scholar 

  35. J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65 137 (1990).

    Article  Google Scholar 

  36. J. L. Lebowitz, M. K. Phani, and D. F. Styer, J. Stat. Phys. 38 413 (1985).

    Article  Google Scholar 

  37. J. F. Fernández and J. Oitmaa, J. Phys. C8, 1549 (1988).

    Google Scholar 

  38. J. Oitmaa and J. F. Fernández, Phys. Rev. B39 11920 (1989).

    Google Scholar 

  39. M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).

    Article  Google Scholar 

  40. A. Arrot, Phys. Rev. B31 2951 (1985).

    Google Scholar 

  41. M. Fähnle and J. Souletie, J. Phys. C17, L469 (1984); Phys. Rev. B32 3328 (1985); Phys. Stat. Sol. 138, 181 (1986).

    Google Scholar 

  42. C. Lamers and W. Schweika, ICNS’91 Oxford, to be published in Physica B.

    Google Scholar 

  43. F. Ducastelle, ICNS’91 Oxford, to be published in Physica B.

    Google Scholar 

  44. E. Domany, Y. Shnidman and D. Mukamel, J. Phys. C: Solid State Phys. 15 L495 (1982).

    Article  Google Scholar 

  45. R. Brout, Phase Transitions, Benjamin, New York, 1965.

    Google Scholar 

  46. M. A. Krivoglaz and A. A. Smirnov, The Theory of Order-Disorder in Alloys, MacDonald, London, 1964; M. A. Krivoglaz, Theory of X-Ray and Thermal Neutron Scattering by Real Crystals, Plenum Press, New York, 1969.

    Google Scholar 

  47. S. C. Moss and P. C. Clapp, Phys. Rev. 171 764 (1968).

    Article  Google Scholar 

  48. R. Lipowsky, Phys. Rev. Lett. 49 1575 (1982).

    Article  Google Scholar 

  49. R. Lipowsky and W. Speth, Phys. Rev. B28 3983 (1983).

    Google Scholar 

  50. R. Lipowsky, J. Appl. Phys. 55 2485 (1984).

    Article  Google Scholar 

  51. R. Lipowsky, Ferroelectrics 73 69 (1987).

    Article  Google Scholar 

  52. K. Binder in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz, Academic Press, New York, 1983. Vol. 8, p. 1.

    Google Scholar 

  53. J. M. Sanchez and J. L. Morán-López, Phys. Rev. B32 3534 (1985).

    Google Scholar 

  54. J.M. Sanchez and J. L. Morán-López, Surf. Sci. Lett. 157 297 (1985).

    Article  Google Scholar 

  55. H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz, Academic Press, New York, 1986. Vol. 10, p. 75.

    Google Scholar 

  56. K. Binder and D. P. Landau, Physica (Amsterdam) 163A 17 (1990).

    Google Scholar 

  57. S. Dietrich, Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz, Academic Press, New York, 1986. Vol. 12, p. 1.

    Google Scholar 

  58. D. M. Kroll and G. Gompper, Phys. Rev. B36 7078 (1987).

    Google Scholar 

  59. G. Gompper and D. M. Kroll, Phys. Rev. B38 459 (1988).

    Google Scholar 

  60. D. M. Kroll and G. Gompper, Phys. Rev. B39 433 (1989).

    Google Scholar 

  61. W. Helbing, B. Dünweg, K. Binder, and D. P. Landau, Z. Physik B, (1990).

    Google Scholar 

  62. W. Schweika, K. Binder, and D. P. Landau, Phys. Rev. Lett. 65 3321 (1990).

    Article  Google Scholar 

  63. Y. Teraoka, Surface Sci. 232 193 (1990).

    Article  Google Scholar 

  64. D. A. Contreras-Solorio, F. Mejía-Lira, J. M. Sanchez, and J. L. Morán-López, Phys. Rev. B38 4955 (1988).

    Google Scholar 

  65. D. A. Contreras-Solorio, F. Mejía-Lira, J. M. Sanchez, and J. L. Morán-López, Phys. Rev. B38 11481 (1988).

    Google Scholar 

  66. B. Dünweg and K. Binder, Phys. Rev. B36 6935 (1987).

    Google Scholar 

  67. V. Pierron-Bohnes, M. C. Cadeville, A. Finel, O. Schäpf, J. Phys. Condens. Matter. 1 247 (1991).

    Google Scholar 

  68. W. Schweika, M. Monkenbush, and A. Ackerman, Physica B156& 157 78 (1989).

    Google Scholar 

  69. W. Schweika, Mat. Res. Soc. Symp. Proc. 166 249 (1990).

    Article  Google Scholar 

  70. F. Schmid and K. Binder, to be published.

    Google Scholar 

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Schweika, W. (1992). Monte Carlo Simulation of Order-Disorder Phenomena in Binary Alloys. In: Morán-López, J.L., Mejía-Lira, F., Sanchez, J.M. (eds) Structural and Phase Stability of Alloys. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3382-5_4

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  • DOI: https://doi.org/10.1007/978-1-4615-3382-5_4

  • Publisher Name: Springer, Boston, MA

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